<?xml version="1.0" encoding="UTF-8" ?>
<?xml-stylesheet type="text/xsl" href="https://communities.bentley.com/cfs-file/__key/system/syndication/rss.xsl" media="screen"?><rss version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/"><channel><title>01. How to apply Kanti Mahajan theory of Vortex Shedding</title><link>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51014/01-how-to-apply-kanti-mahajan-theory-of-vortex-shedding</link><description /><dc:language>en-US</dc:language><generator>Telligent Community 12</generator><item><title>01. How to apply Kanti Mahajan theory of Vortex Shedding</title><link>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51014/01-how-to-apply-kanti-mahajan-theory-of-vortex-shedding</link><pubDate>Tue, 18 Aug 2020 14:06:50 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:31f1293b-21b3-4474-a63b-84fbb9a5c3c8</guid><dc:creator>JamieP</dc:creator><comments>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51014/01-how-to-apply-kanti-mahajan-theory-of-vortex-shedding#comments</comments><description>Current Revision posted to AutoPIPE Wiki by JamieP on 8/18/2020 2:06:50 PM&lt;br /&gt;
&lt;p&gt;Wind induced vibrations on tall vessels are a concern and AutoPIPE Vessel currentley has two methods to address this design consideration.&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;Obtain first the natural frequency &amp;lsquo;f&amp;rsquo; of your vessel&lt;/li&gt;
&lt;li&gt;Check for vibration possibility&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;lt;=20, issue message in report &amp;ldquo;Vibration analysis necessary to be performed as W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;lt;=20&amp;rdquo;&lt;/p&gt;
&lt;p&gt;vibration analysis must be performed and proceed to step 3&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;where W= corroded wt. in lb, L=length in ft., Dr=average internal diameter of top half of the structure in ft.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;gt;20, issue message in report &amp;ldquo;Vibration analysis not necessary to be performed as W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;gt;20&amp;rdquo;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="3"&gt;
&lt;li&gt;Perform stability investigation,&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Calculate damping factor D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt;=W&amp;delta;/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Default value of &amp;delta; = 0.03 (Table 3)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;lt;= 0.75, issue message in report &amp;ldquo;system is unstable and vortex shedding vibration analysis is required as D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;lt;= 0.75&amp;rdquo;, proceed to step 4&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;gt; 0.75, issue message in report &amp;ldquo;Vortex shedding vibration analysis not necessary to be performed as D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;gt; 0.75&amp;rdquo;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="4"&gt;
&lt;li&gt;Calculate critical wind velocity being where &lt;em&gt;S&lt;/em&gt; = 0.226 (Strouhal number)&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Justification: In the book this formula appears as&amp;nbsp; &lt;/em&gt;&lt;em&gt;&amp;nbsp;&lt;/em&gt;&lt;em&gt;in mph, but Dr is introduced in feet, f in Hz, so the number of Strouhal is affected by a conversion factor from feet to miles and hours to seconds. To reverse this change and work in consistent units we have to divide by 1.466 (1mph = 5280/3600 = 1.466 ft/s). And to place S in the denominator, we inverse the coefficient: &lt;/em&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="5"&gt;
&lt;li&gt;Calculate maximum wind velocity at top of the structure (H = 10m or 30ft)&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;V&lt;sub&gt;&lt;span style="font-size:small;"&gt;w&lt;/span&gt;&lt;/sub&gt; =V&lt;sub&gt;&lt;span style="font-size:small;"&gt;b&lt;/span&gt;&lt;/sub&gt;(L/H)&lt;sup&gt;&lt;span style="font-size:small;"&gt;0.143 &lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Where V&lt;sub&gt;&lt;span style="font-size:small;"&gt;b&lt;/span&gt;&lt;/sub&gt; = wind velocity at H&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="6"&gt;
&lt;li&gt;Apply gust factor, 1.3 to obtain maximum gust velocity = 1.3V&lt;sub&gt;&lt;span style="font-size:small;"&gt;w&lt;/span&gt;&lt;/sub&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="7"&gt;
&lt;li&gt;If V&lt;sub&gt;&lt;span style="font-size:small;"&gt;c &lt;/span&gt;&lt;/sub&gt;&amp;lt;=maximum gust velocity, perform amplitude calculations go to step 8.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If V&lt;sub&gt;&lt;span style="font-size:small;"&gt;c &lt;/span&gt;&lt;/sub&gt;&amp;gt; maximum gust velocity, issue message in report &amp;ldquo;Vibration amplitude no need to be calculated as V&lt;sub&gt;&lt;span style="font-size:small;"&gt;c &lt;/span&gt;&lt;/sub&gt;&amp;gt; maximum gust velocity&amp;rdquo;.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="8"&gt;
&lt;li&gt;Calculate amplitude of maximum dynamic deflection, Z=L&lt;sup&gt;&lt;span style="font-size:small;"&gt;5&lt;/span&gt;&lt;/sup&gt;V&lt;span style="font-size:small;"&gt;&lt;sub&gt;C&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;/span&gt;/W &amp;delta; D&lt;sub&gt;&lt;span style="font-size:small;"&gt;r &lt;/span&gt;&lt;/sub&gt;(10)&lt;sup&gt;&lt;span style="font-size:small;"&gt;-6&lt;/span&gt;&lt;/sup&gt; (0.00243) in.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="9"&gt;
&lt;li&gt;Check if Z &amp;lt; Maximum Deflection input by user, issue message in report &amp;ldquo;structure is safe:amplitude of maximum dynamic deflection &amp;lt; maximum allowable deflection&amp;rdquo;&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If Z&amp;gt; Maximum Deflection input by user, issue message in report &amp;ldquo;structure is unsafe:amplitude of maximum dynamic deflection exceeds maximum allowable deflection, please modify design&amp;rdquo;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Reference: Kanti Mahajan, PE. (1979). &lt;em&gt;Design of Process Equipment&lt;/em&gt;. Tulsa, OK: Pressure Vessel Handbook Publishing.&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: Mahajan, vortex shedding&lt;/div&gt;
</description></item><item><title>01. How to apply Kanti Mahajan theory of Vortex Shedding</title><link>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51014/01-how-to-apply-kanti-mahajan-theory-of-vortex-shedding/revision/1</link><pubDate>Tue, 18 Aug 2020 14:06:21 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:31f1293b-21b3-4474-a63b-84fbb9a5c3c8</guid><dc:creator>JamieP</dc:creator><comments>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51014/01-how-to-apply-kanti-mahajan-theory-of-vortex-shedding#comments</comments><description>Revision 1 posted to AutoPIPE Wiki by JamieP on 8/18/2020 2:06:21 PM&lt;br /&gt;
&lt;p&gt;Wind induced vibrations on tall vessels are a concern and AutoPIPE Vessel currentley has two methods to address this design consideration.&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;Obtain first the natural frequency &amp;lsquo;f&amp;rsquo; of your vessel&lt;/li&gt;
&lt;li&gt;Check for vibration possibility&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;lt;=20, issue message in report &amp;ldquo;Vibration analysis necessary to be performed as W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;lt;=20&amp;rdquo;&lt;/p&gt;
&lt;p&gt;vibration analysis must be performed and proceed to step 3&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;where W= corroded wt. in lb, L=length in ft., Dr=average internal diameter of top half of the structure in ft.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;gt;20, issue message in report &amp;ldquo;Vibration analysis not necessary to be performed as W/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2 &lt;/span&gt;&lt;/sup&gt;&amp;gt;20&amp;rdquo;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="3"&gt;
&lt;li&gt;Perform stability investigation,&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Calculate damping factor D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt;=W&amp;delta;/LDr&lt;sup&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Default value of &amp;delta; = 0.03 (Table 3)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;lt;= 0.75, issue message in report &amp;ldquo;system is unstable and vortex shedding vibration analysis is required as D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;lt;= 0.75&amp;rdquo;, proceed to step 4&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;gt; 0.75, issue message in report &amp;ldquo;Vortex shedding vibration analysis not necessary to be performed as D&lt;sub&gt;&lt;span style="font-size:small;"&gt;F&lt;/span&gt;&lt;/sub&gt; &amp;gt; 0.75&amp;rdquo;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="4"&gt;
&lt;li&gt;Calculate critical wind velocity being where &lt;em&gt;S&lt;/em&gt; = 0.226 (Strouhal number)&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Justification: In the book this formula appears as&amp;nbsp; &lt;/em&gt;&lt;em&gt;&amp;nbsp;&lt;/em&gt;&lt;em&gt;in mph, but Dr is introduced in feet, f in Hz, so the number of Strouhal is affected by a conversion factor from feet to miles and hours to seconds. To reverse this change and work in consistent units we have to divide by 1.466 (1mph = 5280/3600 = 1.466 ft/s). And to place S in the denominator, we inverse the coefficient: &lt;/em&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="5"&gt;
&lt;li&gt;Calculate maximum wind velocity at top of the structure (H = 10m or 30ft)&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;V&lt;sub&gt;&lt;span style="font-size:small;"&gt;w&lt;/span&gt;&lt;/sub&gt; =V&lt;sub&gt;&lt;span style="font-size:small;"&gt;b&lt;/span&gt;&lt;/sub&gt;(L/H)&lt;sup&gt;&lt;span style="font-size:small;"&gt;0.143 &lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;
&lt;p&gt;Where V&lt;sub&gt;&lt;span style="font-size:small;"&gt;b&lt;/span&gt;&lt;/sub&gt; = wind velocity at H&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="6"&gt;
&lt;li&gt;Apply gust factor, 1.3 to obtain maximum gust velocity = 1.3V&lt;sub&gt;&lt;span style="font-size:small;"&gt;w&lt;/span&gt;&lt;/sub&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="7"&gt;
&lt;li&gt;If V&lt;sub&gt;&lt;span style="font-size:small;"&gt;c &lt;/span&gt;&lt;/sub&gt;&amp;lt;=maximum gust velocity, perform amplitude calculations go to step 8.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If V&lt;sub&gt;&lt;span style="font-size:small;"&gt;c &lt;/span&gt;&lt;/sub&gt;&amp;gt; maximum gust velocity, issue message in report &amp;ldquo;Vibration amplitude no need to be calculated as V&lt;sub&gt;&lt;span style="font-size:small;"&gt;c &lt;/span&gt;&lt;/sub&gt;&amp;gt; maximum gust velocity&amp;rdquo;.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="8"&gt;
&lt;li&gt;Calculate amplitude of maximum dynamic deflection, Z=L&lt;sup&gt;&lt;span style="font-size:small;"&gt;5&lt;/span&gt;&lt;/sup&gt;V&lt;span style="font-size:small;"&gt;&lt;sub&gt;C&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;/span&gt;/W &amp;delta; D&lt;sub&gt;&lt;span style="font-size:small;"&gt;r &lt;/span&gt;&lt;/sub&gt;(10)&lt;sup&gt;&lt;span style="font-size:small;"&gt;-6&lt;/span&gt;&lt;/sup&gt; (0.00243) in.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="9"&gt;
&lt;li&gt;Check if Z &amp;lt; Maximum Deflection input by user, issue message in report &amp;ldquo;structure is safe:amplitude of maximum dynamic deflection &amp;lt; maximum allowable deflection&amp;rdquo;&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If Z&amp;gt; Maximum Deflection input by user, issue message in report &amp;ldquo;structure is unsafe:amplitude of maximum dynamic deflection exceeds maximum allowable deflection, please modify design&amp;rdquo;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Reference: Kanti Mahajan, PE. (1979). &lt;em&gt;Design of Process Equipment&lt;/em&gt;. Tulsa, OK: Pressure Vessel Handbook Publishing.&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;
</description></item></channel></rss>